Hi Chris,
There are normally 4 alpha genes, found in pairs on each of chromosome 16. When there is an alpha triplication, one of these pairs has one normal alpha gene and a triplicated (aaa) gene as its "partner" on that chromosome. You might see this written as alpha alpha/alpha alpha alpha 3.7. As you suggested, there is not a lot of difference between this and normal alpha genes. However, when combined with beta thalassemia, there are a wide range of possible outcomes depending on the specific beta mutation.
As long as this is your child's only thal mutation or deletion, the most you should see is a mild anemia, as is sometimes seen with alpha thal trait, where two genes are affected. However, the alpha triplication can vary in phenotype, so it can result in different outcomes. As long as no other thal gene is involved, it should never be a serious, transfusion requiring condition. Has the child shown any signs of anemia, lethargy, for example?